Radio positioning method based on multi-epoch observed quantity combination and multi-model combination weighting
Through the combined multi-epoch observation and multi-model combination empowerment method, the problem of inaccurate radio navigation positioning caused by insufficient single-epoch observation is solved, and the continuous and reliable positioning of the receiver is achieved when insufficient observation is insufficient, improving positioning accuracy and reliability.
Patent Information
- Application Number
- CN202510626759.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-15
- Publication Date
- 2025-08-15
AI Technical Summary
In radio navigation positioning, when single epoch observation is insufficient, conventional methods lead to underdetermining the solution equation or deteriorating the positioning accuracy, making it impossible to achieve reliable receiver positioning.
Through the method of multi-epoch observation combined and multi-model combination empowerment, a trajectory model of different motion types and orders is constructed using time-invariant trajectory parameters, the time-varying position and velocity of the receiver are fitted, the residual judgment statistics are calculated, and the results that do not meet the threshold are eliminated, and the model combination weighting is finally carried out to obtain the positioning result.
In the case of short observation time insufficient, the continuous and reliable positioning of the receiver is achieved, the positioning accuracy and reliability are improved, and the accuracy of the positioning results are ensured through multi-epoch observation expansion and multi-model fitting error judgment.
Smart Images
Figure CN120491122A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a radio positioning method combining multi-epoch observations with multi-model combination weighting, and belongs to the fields of signal processing, navigation positioning, and aerospace measurement and control. Background Art
[0002] Radio navigation positioning, including satellite navigation, ground-based navigation, and cellular signal navigation, offers advantages such as 24 / 7 operation, long range, and high positioning accuracy, making it widely used in numerous civil and military fields. In radio navigation, a receiver receives radio signals from various anchor points, obtaining relative distance and velocity measurements from these anchor points to perform a positioning solution. To meet these requirements, the number of available anchor points must be greater than the number of unknowns to be solved. In practice, due to factors such as anchor point equipment failures and obstruction, the receiver may temporarily run out of available observations.
[0003] Conventional single-point positioning methods based on range intersections use single-epoch range observations to construct and solve positioning equations. If the number of single-epoch observations is less than the number of unknowns in the positioning solution, the solution equations will be underdetermined, resulting in positioning failure. Filtering methods use historical epoch positioning results to predict the receiver position and then use single-epoch observations to update the predicted position. Insufficient single-epoch observations will result in poor position updates and degraded positioning accuracy. Summary of the Invention
[0004] The purpose of the present invention is to provide a radio positioning method that combines multi-epoch observations with multi-model combination weighting, which can achieve continuous and reliable positioning of the receiver when the observations are insufficient for a short time.
[0005] The technical solutions for implementing the present invention are as follows:
[0006] In a first aspect, the present invention provides a radio positioning method for combining multi-epoch observations with multi-model weighting, the specific process of which is as follows:
[0007] Step 1: Obtain the relative observation h between the N epoch anchor points and the moving target;
[0008] Step 2: Use the time-invariant trajectory parameters to fit the time-varying position and velocity of the moving target and construct a moving target trajectory model with different motion types and different trajectory parameter orders;
[0009] Step 3: For each moving target trajectory model, use it to represent the time-varying position and velocity of the moving target in the observation h, establish and solve the positioning objective function of each trajectory model, obtain the fitting coefficients in the moving target trajectory model, and infer the time-varying position and velocity of the moving target based on the fitting coefficients;
[0010] Step 4: Calculate the corresponding observation residual according to the time-varying position and speed of the moving target, and further calculate the residual judgment statistic, and eliminate the position and speed whose residual judgment statistic is greater than the set threshold;
[0011] Step 5: Combine and weight the time-varying positions and velocities of the moving targets that are not eliminated to obtain the final receiver positioning result.
[0012] Optionally, the moving target trajectory model of the present invention
[0013]
[0014] Among them, α l , β l are the position and velocity fitting polynomial coefficients, the instantaneous invariant trajectory parameters, and ξ l,t is the orthogonal polynomial basis, and L is the fitting polynomial coefficient.
[0015] Optionally, the dynamic trajectory models of different motion types and different orders L described in the present invention include polynomial trajectory models and quadratic motion models. The polynomial trajectory model includes a first-order uniform speed model, a second-order uniform acceleration model, and a second-order variable acceleration motion model. The quadratic motion model includes a first-order uniform speed turning model and a second-order constant turning rate and speed model.
[0016] Optionally, the present invention uses it to express the time-varying position and velocity of the moving target in the observation h as follows:
[0017]
[0018] Optionally, the objective function of the present invention is:
[0019]
[0020] Among them, f({α,β} L ) represents the mapping function between the position and velocity fitting model coefficients and the relative observation h, and W is the covariance matrix of the distance and velocity measurement noise ε.
[0021] Optionally, in step 4 of the present invention, the corresponding observation residual is calculated based on the time-varying position and speed of the moving target, and the residual decision statistic is further calculated. The specific process is:
[0022] Based on the fitting coefficients, the time-varying position and velocity of the moving target are expressed as: Then the residual of the observed distance from the visible anchor point at the current epoch is Velocity observation residual for:
[0023]
[0024] The residual judgment statistic ε is obtained by weighted square of all distance and speed residuals in N time periods. p , ε v .
[0025] Optionally, the specific process of step 5 of the present invention is:
[0026] According to the model likelihood, the trajectory model weight ω under different epochs can be determined L,t :
[0027] According to the weights, the positioning results of different trajectory models are combined and weighted to obtain the final receiver positioning and speed determination results.
[0028] In a second aspect, the present invention provides a radio positioning device that combines multi-epoch observations with multi-model weighting, comprising:
[0029] The observation acquisition module is used to obtain the relative observation h between N epoch anchor points and the moving target;
[0030] The target trajectory fitting module uses time-invariant trajectory parameters to fit the time-varying position and velocity of the moving target and constructs trajectory models of moving targets with different motion types and different trajectory parameter orders;
[0031] The target positioning module uses each moving target trajectory model to represent the time-varying position and velocity of the moving target in the observation quantity h, establishes and solves the positioning target function for each trajectory model, obtains the fitting coefficients in the moving target trajectory model, and infers the time-varying position and velocity of the moving target based on the fitting coefficients;
[0032] The residual statistical judgment module is used to calculate the corresponding observation residual according to the time-varying position and speed of the moving target, and further calculate the residual judgment statistic, and eliminate the position and speed whose residual judgment statistic is greater than the set threshold value;
[0033] The positioning result combination module is used to combine and weight the time-varying positions and velocities of the moving targets that have not been eliminated to obtain the final receiver positioning result.
[0034] Beneficial effects:
[0035] This method expands the number of observations by integrating historical epochs and exploiting the short-term stationary nature of receiver trajectories. It uses multiple trajectory models of varying types and orders, each with time-invariant parameters, to fit the receiver's time-varying position and velocity, compressing the number of variables and ensuring fitting accuracy. Each trajectory model is then independently positioned and solved, and observation residuals are calculated based on the positioning results, with the model fitting accuracy assessed. Finally, models with satisfactory fitting accuracy are weighted and fused, enabling continuous and reliable positioning of the receiver even when observations are insufficient for a short period of time. BRIEF DESCRIPTION OF THE DRAWINGS
[0036] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.
[0037] Figure 1 It is a flowchart of the method of the present invention;
[0038] Figure 2 Schematic diagram of merging multi-epoch observations in the present invention. DETAILED DESCRIPTION
[0039] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.
[0040] It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments may be combined with each other; and, based on the embodiments in this disclosure, all other embodiments obtained by persons of ordinary skill in the art without creative work are within the scope of protection of this disclosure.
[0041] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this disclosure, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.
[0042] The embodiment of the present application provides a radio positioning method for combining multi-epoch observations with multi-model combination weighting, including five steps: merging multi-epoch observations, selecting a trajectory model set, fitting receiver trajectories, judging model fitting errors, and weighting multi-model fitting results. Figure 1 Specifically:
[0043] Step 1: Obtain the relative observation h between the N epoch anchor points and the moving target;
[0044] Step 2: Use the time-invariant trajectory parameters to fit the time-varying position and velocity of the moving target and construct a moving target trajectory model with different motion types and different trajectory parameter orders;
[0045] Step 3: For each moving target trajectory model, use it to represent the time-varying position and velocity of the moving target in the observation h, establish and solve the positioning objective function of each trajectory model, obtain the fitting coefficients in the moving target trajectory model, and infer the time-varying position and velocity of the moving target based on the fitting coefficients;
[0046] Step 4: Calculate the corresponding observation residual according to the time-varying position and speed of the moving target, and further calculate the residual judgment statistic, and eliminate the position and speed whose residual judgment statistic is greater than the set threshold;
[0047] Step 5: Combine and weight the time-varying positions and velocities of the moving targets that are not eliminated to obtain the final receiver positioning result.
[0048] This embodiment uses multiple trajectory models to fit the receiver's short-term trajectory, combines historical epoch observation information from before the period of insufficient observations to solve the trajectory model parameters, and judges the model fitting error in real time. This improves positioning continuity under short-term insufficient observations and ensures positioning reliability.
[0049] Each step of the present invention is described in detail below:
[0050] (1) Merging of multi-epoch observations
[0051] When the number of observations in a single epoch is less than the number of unknowns required for positioning solution, positioning solution cannot be obtained. To increase the number of observations, the present invention combines the ranging and velocity measurement results between the receiver and the anchor point in multiple epochs (including epochs with sufficient historical observations and epochs with insufficient observations).
[0052] Assume that the number of anchor points is M and the number of receiver joint historical epochs is N. For epoch t, the receiver can receive t The observations of anchor points can be combined to express the observation information of multiple epochs as
[0053]
[0054] Among them, ρ 1,1 represents the distance observation between the receiver and anchor point 1 at epoch t=1, f 1,1It represents the velocity observation of the receiver and anchor point 1 at epoch t=1. The above observations are all data that can be directly obtained.
[0055] ρ i,t =||p t -s i ||+n ρ
[0056]
[0057] Among them, ρ i,t and f i,t Respectively represent the relative distance and speed between the anchor point i and the moving target at epoch t, where Represents the three-dimensional position of the moving target, () T represents the transpose operation, represents the 3D position of the i-th stationary anchor point, v t Indicates the three-dimensional velocity of the moving target, n ρ 、n f Respectively represent the distance and speed measurement errors. In the formula, p t and v t is the unknown parameter to be solved.
[0058] In a time period of length N, the number of true distance and true velocity observations obtained by the receiver at each epoch is D t The total number of observations obtained is When the visible anchor point remains unchanged during the period of insufficient observations, the receiver can only obtain observations from two fixed directions and can only establish two-dimensional spatial constraints on the receiver position to be determined.
[0059] Therefore, it is necessary to combine multiple historical observations to obtain sufficient epochs, use historical observations to increase the three-dimensional spatial constraints on the receiver position, improve the solution precision factor, and improve positioning accuracy. Figure 2 As shown:
[0060] In the present invention, the number of epochs of the joint historical observation quantity is set to the length of the period of insufficient observation quantity at the current moment, so that more than half of the equations in the multi-epoch joint solution equation group constrain the three-dimensional space of the receiver position, thereby improving positioning accuracy.
[0061] (2) Trajectory model set selection
[0062] Combining multi-epoch observations effectively increases the number of observations. Because receiver positions vary over time, combining multi-epoch observations leads to a proportional increase in the number of variables to be solved. Therefore, it is necessary to fit the time-varying positions with time-invariant trajectory parameters to correlate the unknowns in the multi-epoch solution and reduce the number of variables to be solved.
[0063] Without loss of generality, we use pt Denote the three-dimensional position of the receiver at epoch t, with v t represents the three-dimensional velocity of the receiver at epoch t. The time-varying position and velocity of the receiver in a time period of length N are fitted with a trajectory model. The orthogonal polynomial trajectory model h(α1,...,α L ,β1,...,β L ) as an example, the trajectory model fitting results of the receiver's time-varying position and velocity are:
[0064]
[0065] Among them, α l , β l are the fitting polynomial coefficients of position and velocity, ξ l,t is an orthogonal polynomial basis. Through the trajectory model, the receiver’s time-varying position p t , time-varying velocity v t The time-invariant parameter α l , β l , l∈{1,...,L}. The number of solution variables of the trajectory model is only related to the variables to be solved in the trajectory model, that is, multiple epochs share the same solution variables, reducing the number of solution variables.
[0066] In order to avoid the mismatch between a single trajectory model and the receiver motion characteristics, which leads to large fitting errors and rapid degradation of positioning performance, the present invention constructs dynamic trajectory models with different motion types and different orders L (including polynomial trajectory models and quadratic motion models) to construct a trajectory model set. Multiple trajectory models in the model set are used to jointly fit the receiver's position and velocity. The resulting trajectory model set covers a wide range of receiver motion characteristics, improving receiver trajectory fitting accuracy and reducing positioning error compared to using a single model. The polynomial trajectory models in the model set include a first-order constant velocity model (CV), a second-order uniform acceleration model (CA), and a second-order variable acceleration motion model (Singer). The quadratic motion models in the model set include a first-order constant turn model (CT) and a second-order constant turn rate and velocity model (CTRV).
[0067] (3) Receiver trajectory fitting
[0068] After constructing the trajectory model set, each model in the model set is used to fit the receiver's short-term trajectory. For example, after substituting into the trajectory model, the distance observation r obtained by the receiver at epoch t from the anchor point m is m,t , velocity observation v m,t It can be expressed as:
[0069] r m,t =||p t -pm ||2+ε m,t (7)
[0070]
[0071] Among them, p m Represents the known position of the anchor point m. ε m,t 、 is the distance and speed measurement noise, which obeys zero-mean Gaussian distribution.
[0072] The model Substituting the fitting results of the receiver's time-varying position and velocity into the true distance and true velocity observation equations, we can obtain:
[0073]
[0074] Among them, f ρ (α1...,α L ,β1...,β L ),f f (α1...,α L ,β1...,β L ) represents the parameters α1...,α L ,β1...,β L Nonlinear functions mapped to distances,observations.
[0075] Combining the above formulas, we can get the multi-epoch observations and the unknowns to be solved {α, β} L =[α1...,α L ,β1...,β L ], expressed as:
[0076] h=f({α,β} L )+ε (11)
[0077] Among them, f({α,β} L ) represents the mapping function between the position and velocity fitting model coefficients and the relative observation h, and ε represents the observation noise.
[0078] Thus, the positioning objective function can be constructed for each trajectory model:
[0079]
[0080] Where W is the covariance matrix of the distance and speed measurement noise ε. The objective function can be solved by the Gauss-Newton iteration method to obtain the trajectory model solution variables Based on the model parameters, the time-varying position and velocity of the receiver are deduced as
[0081] (4) Model fitting error judgment
[0082] To ensure the reliability of the positioning results, it is necessary to eliminate the model with large trajectory fitting error to ensure the positioning accuracy. The trajectory model can be used to calculate the residual of the distance between the current epoch and the visible anchor point based on the positioning results. Velocity observation residual
[0083]
[0084] The observation residual reflects the difference between the true distance and true speed calculated based on the trajectory model positioning results at the current epoch and the actual true distance and true speed observations. A small residual indicates that the model positioning result is close to the receiver's true position, otherwise it indicates that the model positioning result is unreliable. The residual judgment statistic ε is obtained by weighting the square of all distance and speed residuals in N time periods. p , ε v .
[0085] According to the positioning accuracy requirements of the receiver, the residual threshold is set to judge the model positioning and speed errors. If ε p , ε v If both are less than the threshold, it means that the positioning and speed control results of the model meet the accuracy requirements. Otherwise, the model is unreliable for the flight trajectory fitting result. If no model in the trajectory model set passes the error judgment threshold, it means that all models are unreliable and the positioning result is invalid. If a model passes the threshold judgment, then go to step (5) to perform weighted fusion on the model positioning results.
[0086] (5) Combination weighting of multi-model fitting results
[0087] Each model, determined by thresholding, represents the fitting result for different motion characteristics of the receiver. By weighted fusion of the positioning results of different models, the optimal fitting of the flight trajectory is achieved.
[0088] The present invention adopts the model likelihood index to fuse the positioning results of different models. Based on the true distance and true speed residuals, each trajectory model can calculate the likelihood of the current epoch and the actual flight position and speed. The model {α, β} of order L is used to calculate the likelihood of the current epoch and the actual flight position and speed. L For example, the model likelihood under epoch t is for:
[0089]
[0090] According to the model likelihood, the trajectory model weight ω under different epochs can be determined L,t :
[0091]
[0092] According to the weights, the positioning results of different trajectory models are combined and weighted to obtain the final receiver positioning and speed determination results:
[0093]
[0094] The embodiment of the present application provides a radio positioning device that combines multi-epoch observations with multi-model weighting, including:
[0095] The observation acquisition module is used to obtain the relative observation h between N epoch anchor points and the moving target;
[0096] The target trajectory fitting module uses time-invariant trajectory parameters to fit the time-varying position and velocity of the moving target and constructs trajectory models of moving targets with different motion types and different trajectory parameter orders;
[0097] The target positioning module uses each moving target trajectory model to represent the time-varying position and velocity of the moving target in the observation quantity h, establishes and solves the positioning target function for each trajectory model, obtains the fitting coefficients in the moving target trajectory model, and infers the time-varying position and velocity of the moving target based on the fitting coefficients;
[0098] The residual statistical judgment module is used to calculate the corresponding observation residual according to the time-varying position and speed of the moving target, and further calculate the residual judgment statistic, and eliminate the position and speed whose residual judgment statistic is greater than the set threshold value;
[0099] The positioning result combination module is used to combine and weight the time-varying positions and velocities of the moving targets that have not been eliminated to obtain the final receiver positioning result.
[0100] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.
Claims
1. A radio positioning method combining multi-epoch observations with multi-model weighting, characterized in that: The specific process is: Step 1: Obtain the relative observation h between the N epoch anchor points and the moving target; Step 2: Use the time-invariant trajectory parameters to fit the time-varying position and velocity of the moving target and construct a moving target trajectory model with different motion types and different trajectory parameter orders; Step 3: For each moving target trajectory model, use it to represent the time-varying position and velocity of the moving target in the observation h, establish and solve the positioning objective function of each trajectory model, obtain the fitting coefficients in the moving target trajectory model, and infer the time-varying position and velocity of the moving target based on the fitting coefficients; Step 4: Calculate the corresponding observation residual according to the time-varying position and speed of the moving target, and further calculate the residual judgment statistic, and eliminate the position and speed whose residual judgment statistic is greater than the set threshold; Step 5: Combine and weight the time-varying positions and velocities of the moving targets that are not eliminated to obtain the final receiver positioning result.
2. The radio positioning method of claim 1, wherein: The moving target trajectory model Among them, α l , β l are the position and velocity fitting polynomial coefficients, the instantaneous invariant trajectory parameters, and ξ l,t is the orthogonal polynomial basis, and L is the fitting polynomial coefficient.
3. The radio positioning method of claim 2, wherein the method comprises: The dynamic trajectory models of different motion types and different orders L include polynomial trajectory models and quadratic motion models. The polynomial trajectory model includes a first-order uniform speed model, a second-order uniform acceleration model, and a second-order variable acceleration motion model. The quadratic motion model includes a first-order uniform speed turning model and a second-order constant turning rate and speed model.
4. The radio positioning method of claim 2, wherein the method comprises: The time-varying position and velocity of the moving target in the observation h are expressed as follows:
5. The radio positioning method of claim 4, characterized in that: The objective function is: Among them, f({α,β} L ) represents the mapping function between the position and velocity fitting model coefficients and the relative observation h, and W is the covariance matrix of the distance and velocity measurement noise ε.
6. The radio positioning method of claim 1, wherein: The fourth step is to calculate the corresponding observation residual according to the time-varying position and speed of the moving target, and further calculate the residual decision statistic. The specific process is as follows: Based on the fitting coefficients, the time-varying position and velocity of the moving target are expressed as: Then the residual of the observed distance from the visible anchor point at the current epoch is Velocity observation residual for: Among them, p m Represents the position of the anchor point m; The residual judgment statistic ε is obtained by weighted square of all distance and speed residuals in N time periods. p , ε v .
7. The radio positioning method of claim 1, wherein: The specific process of step five is: According to the model likelihood, the trajectory model weight ω under different epochs can be determined L,t : According to the weights, the positioning results of different trajectory models are combined and weighted to obtain the final receiver positioning and speed determination results.
8. A radio positioning device that combines multi-epoch observations with multi-model weighting, characterized in that: include: The observation acquisition module is used to obtain the relative observation h between N epoch anchor points and the moving target; The target trajectory fitting module uses time-invariant trajectory parameters to fit the time-varying position and velocity of the moving target and constructs trajectory models of moving targets with different motion types and different trajectory parameter orders; The target positioning module uses each moving target trajectory model to represent the time-varying position and velocity of the moving target in the observation quantity h, establishes and solves the positioning target function for each trajectory model, obtains the fitting coefficients in the moving target trajectory model, and infers the time-varying position and velocity of the moving target based on the fitting coefficients; The residual statistical judgment module is used to calculate the corresponding observation residual according to the time-varying position and speed of the moving target, and further calculate the residual judgment statistic, and eliminate the position and speed whose residual judgment statistic is greater than the set threshold value; The positioning result combination module is used to combine and weight the time-varying positions and velocities of the moving targets that have not been eliminated to obtain the final receiver positioning result.
9. The radio positioning method of claim 8, characterized in that: The moving target trajectory model Among them, α l , β l are the position and velocity fitting polynomial coefficients, the instantaneous invariant trajectory parameters, and ξ l,t is the orthogonal polynomial basis, and L is the fitting polynomial coefficient.
10. The radio positioning method of claim 9, characterized in that: The time-varying position and velocity of the moving target in the observation h are expressed as follows: The objective function is: Among them, f({α,β} L ) represents the mapping function between the position and velocity fitting model coefficients and the relative observation h, and W is the covariance matrix of the distance and velocity measurement noise ε.